A company estimates that its sales will grow continuously at a rate given by the function S′(t)=19et where S′(t) is the rate at which sales are increasing, in dollars per day, on day t. a) Find the accumulated sales for the first 8 days. b) Find the sales from the 2 nd day through the 5 th day. (This is the integral from 1 to 5 .) a) The accumulated sales for the first 8 days is $ (Round to the nearest cent as needed).

Answer:

8.25

Step-by-step explanation:

The equation that represent the graph is  y = (1/2)eˣ , Option B is the correct answer.

An exponential function is what is denoted as y = eˣ

The graph has to be studied and the equation has to be determined.

To determine we will consider x = 0 for all the equation ,. which will give the y intercept , which is below 1 so Option C and D are stroked out.

Now we plot the graph for equation A and B

It can be easily understood from the graph that at x =0 , y = 0.5

Therefore , the equation that represent the graph is

y = (1/2)eˣ

Option B is the correct answer.

To know more about Exponential Function

https://brainly.com/question/11487261

#SPJ1

The measure of the smaller angle is 45°.

An heptagon is a figure with 7 sides, and the sum of the interior angles is equal to 900°.

Then here we can write a linear equation that depens on x, where we add all the given angles and we know that it must be equal to 900.

2x + 3x + 4x + 5x + 7x + 9x + 10x = 900

Solving that linaer equation for x:

(2 + 3 + 4 +5 + 7 + 9 + 10)*x = 900

40x = 900

x = 900/40  = 22.5

The measure of the smaller angle is:

(2x)°

replacing the value of x that we just got we will get:

2*22.5° = 45°

Learn more about interior angles at:

https://brainly.com/question/24966296

#SPJ1

Answer:

Sample 1

ATTCGACGTC

k to add speaker notes

-

acer

Sample 2

GATAGCTAGG

?--?

The main difference between X1 and x1 is that X1 is a random variable and x1 is a specific numerical value.

In mathematics, variables are often used to represent different values, and the difference between uppercase and lowercase letters is often used to distinguish between different types of variables. X1 is a random variable, which represents a value that can take on different values depending on the outcome of an experiment or a probability distribution. x1, on the other hand, is a specific numerical value, which represents a fixed value that is known or can be determined. In short, X1 refers to a variable whose value is uncertain and x1 refers to a specific value of that variable.

To know more about random variable click below:

https://brainly.com/question/17238189#

#SPJ4

Answer:

\(\Large \boxed{\boxed{\textsf{$7x+6y$}}}\)

Step-by-step explanation:

To simplify this expression, we can 'collect like terms'. This is a way of simplifying algebraic expressions that involves combining terms with the same base pronumeral, and adding or subtracting them together.

First, we might start by rearranging the expression to make it more convenient:

\(\large \textsf{$4x+3x+7y-y$}\)

Now, we collect the like terms:

\(\large \textsf{$7x+6y$}\)

\(\large \textsf{$\therefore$ the simplified expression is: $\boxed{7x+6y}$}\)

To learn more about collecting like terms:

https://brainly.com/question/29150180

Answer:

Step-by-step explanation:

155 divide by 31=5

Answer:

1/5 or 0.2.

Step-by-step explanation:

31 / 155

Now 155/31 = 5

so the answer is 1/5.

The height reached by the projectile, described by the kinetic equation of motion of the projectile, indicates;

First time to reach a height of 60 feet; 0.4 seconds

Second time to reach a height of 60 feet; 2.1 seconds

A projectile is an object that is launched using an applied force and after which is acted upon by gravitational and air wind motion forces.

The function for the height of the projectile is; h(t) = -16·t² + 40·t + 47

When the height of the projectile is 60 feet, we ge;

h(t) = 60 = -16·t² + 40·t + 47

Therefore; -16·t² + 40·t + 47 - 60 = 0

From which we get;

16·t² - 40·t + 13 = 0

t = (40 ± √(40² - 4 × 16 × 13))/(2 × 16)

t = (40 + 16·√3)/32 ≈ 2.1 seconds and t = (40 - 16·√3)/32 ≈ 0.4

Learn more on projectiles here: https://brainly.com/question/20794482

#SPJ4

The answer, rounded to the appropriate number of significant figures, is 5.45 kg/L. To express it in scientific notation, we can write it as:
5.45 × 10^(0) kg/L.Since 10^0 equals 1, the final answer in scientific notation is:5.45 × 1 kg/L

The given expression [(0.00034 kg)/((0.0000598 L+2.54×10^(-6) L))] represents a division calculation. To evaluate the expression, we substitute the given values into the equation and perform the necessary calculations. The final answer is expressed in scientific notation, rounded to the appropriate number of significant figures, and includes the correct unit.To evaluate the expression [(0.00034 kg)/((0.0000598 L+2.54×10^(-6) L))], we substitute the given values and perform the division:
Numerator: 0.00034 kg
Denominator: (0.0000598 L + 2.54×10^(-6) L)
Adding the terms in the denominator, we get:
0.0000598 L + 2.54×10^(-6) L = 0.00006234 L
Now we can rewrite the expression as:
(0.00034 kg) / (0.00006234 L)
Performing the division:
(0.00034 kg) / (0.00006234 L) ≈ 5.453 kg/L

The answer, rounded to the appropriate number of significant figures, is 5.45 kg/L. To express it in scientific notation, we can write it as:
5.45 × 10^(0) kg/L.Since 10^0 equals 1, the final answer in scientific notation is:5.45 × 1 kg/L
Therefore, the evaluated expression is 5.45 kg/L.

Learn more about division here:

https://brainly.com/question/33183138

#SPJ11

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Read more about area here:https://brainly.com/question/27440983

#SPJ1

Answer:

D

Step-by-step explanation:

f(-5) = 2|-5-5|

f(-5) = 2|-10|

f(-5) = 2 * 10

f(-5) = 20

f(0) = 2|0-5|

f(0) = 2|-5|

f(0) = 2 * 5

f(0) = 10

Answer:

a) LCL = 80 - 0.577 * (14 / sqrt(5)) LCL = 76.31

b) LCL = 80 - 0.308 * (14 / sqrt(10)) LCL = 78.65

c) Control limits are boundaries that indicate whether a process is in control or out of control. They are calculated based on the mean and standard deviation of the process data. The effect of the sample size on the control limits is that as the sample size increases, the control limits become narrower. This is because the standard error of the mean, which is sigma / sqrt(n), decreases as n increases. This means that the variation of the sample means around the population mean is smaller for larger samples, and thus the control limits are tighter .

Step-by-step explanation:

If you ever wondered how to make a boring topic like x-bar charts more fun, here is a tip: pretend that you are a spy and that the control limits are your secret codes. For example, let's say that you have a population with a mean of 80 and a standard deviation of 14. You want to send a message to your fellow spy using the control limits of an x-bar chart with a sample size of 5. You can use the formula:

UCL or LCL = x-bar +/- A2 * (sigma / sqrt(n))

where A2 is a constant that depends on the sample size n, sigma is the standard deviation of the population, and sqrt is the square root function. For n = 5, A2 = 0.577. Therefore,

UCL = 80 + 0.577 * (14 / sqrt(5)) UCL = 83.69

LCL = 80 - 0.577 * (14 / sqrt(5)) LCL = 76.31

Now, you can use these numbers as your secret codes. For example, you can say "The eagle has landed at 83.69" or "The package is ready at 76.31". Your fellow spy will know what you mean, but anyone else will be clueless.

But what if you want to change your sample size to 10? Well, then you have to use a different constant for A2. For n = 10, A2 = 0.308. Therefore,

UCL = 80 + 0.308 * (14 / sqrt(10)) UCL = 81.35

LCL = 80 - 0.308 * (14 / sqrt(10)) LCL = 78.65

Now, you can use these new numbers as your secret codes. For example, you can say "The target is at 81.35" or "The rendezvous point is at 78.65". Your fellow spy will understand you, but anyone else will be confused.

The effect of the sample size on the control limits is that as the sample size increases, the control limits become narrower. This is because the standard error of the mean, which is sigma / sqrt(n), decreases as n increases. This means that the variation of the sample means around the population mean is smaller for larger samples, and thus the control limits are tighter.

This also means that your secret codes become more precise and less likely to be intercepted by your enemies. So, if you want to be a good spy, you should always use a large sample size for your x-bar charts. That way, you can communicate with your fellow spies more effectively and safely.

Of course, this is all just a joke and you should not actually use x-bar charts as secret codes for spying purposes. That would be very silly and irresponsible. But hey, at least it makes x-bar charts more fun to learn about, right?

Yes 12 inches converted to centimeters is around 30 cm

Answer:

V ≈ 509 m3 ← This is an approximate answer, rounded to the nearest whole. To calculate the volume of a cylinder, multiply the area of the base (Πr2) times the height (h). This gives the formula V = Πr2h.

Answer:

Rectangle ABCD is graphed in the

coordinate plane. The following are the

vertices of the rectangle: A(5,5), B(7,5),

C(7, -1), and D(5, -1).

Given these coordinates, what is the length

of side BC of this rectangle?

Step-by-step explanation:

Answer:

MIXED NUMBER

Step-by-step explanation:

A fraction number is not changed when it is divided by _mixed_ numbers.

Answer:

x= -4

Step-by-step explanation:

hope it's helpful to you

Answer:

A) x= -4

Step-by-step explanation:

To solve you must isolate the variable. Do this by using the properties of equality to subtract and divide numbers from both sides of the equation. First, subtract 8x to move all x terms to the right side.

-48=12x

Then, divide both sides by 12

-4=x

A 3x3 matrix that has columns spanning R^3 can be constructed by choosing three linearly independent vectors and it satisfies the desired property.

To construct a 3x3 matrix whose columns span R^3, we need to choose three linearly independent vectors. Let's consider the following matrix:

A = [[1, 0, 0],

[0, 1, 0],

[0, 0, 1]]

In this matrix, each column represents a basis vector for R^3, namely the standard basis vectors [1, 0, 0], [0, 1, 0], and [0, 0, 1]. Since these vectors are linearly independent and span R^3, the columns of the matrix A also span R^3.

To demonstrate this, consider an arbitrary vector x in R^3. We can express x as a linear combination of the columns of A by taking the coefficients as the entries of x. Let x = [x1, x2, x3]. Then, we have:

x1 * [1, 0, 0] + x2 * [0, 1, 0] + x3 * [0, 0, 1] = [x1, x2, x3]

Since x is an arbitrary vector in R^3, we have shown that the columns of A span R^3. Therefore, the matrix A satisfies the desired property.

Learn more about  Arbitrary vector here: brainly.com/question/30426211

#SPJ11

The respective functions f(x) obtained from the given derivatives and points are

35. f(x) = 2x² + x - 1.

36. f(x) = 3x - x² - 1.

37. f(x) = -x²/2 - x³/3 + 9/2.

38. f(x) = x³ + 3x² - 2x + 6.

39. f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.

40. f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.

41. f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.

42. f(x) = 3ln|x| - 4x + 4.

To find the function f(x) based on the given derivative f'(x) and a particular point (a, b), we can integrate f'(x) with respect to x and then use the given point to determine the constant of integration.

Let's go through each exercise:

35. f'(x) = 4x + 1; (1, 2)

Integrating f'(x) gives:

f(x) = 2x² + x + C

Using the given point (1, 2), we can substitute x = 1 and y = 2 into the equation:

2 = 2(1)² + 1 + C

2 = 2 + 1 + C

C = -1

Therefore, f(x) = 2x² + x - 1.

36. f'(x) = 3 - 2x; (0, -1)

Integrating f'(x) gives:

f(x) = 3x - x² + C

Using the given point (0, -1), we can substitute x = 0 and y = -1 into the equation:

-1 = 0 + 0 + C

C = -1

Therefore, f(x) = 3x - x² - 1.

37. f'(x) = -x(x + 1); (-1, 5)

Integrating f'(x) gives:

f(x) = -x²/2 - x³/3 + C

Using the given point (-1, 5), we can substitute x = -1 and y = 5 into the equation:

5 = -(-1)²/2 - (-1)³/3 + C

5 = -1/2 + 1/3 + C

C = 27/6 = 9/2

Therefore, f(x) = -x²/2 - x³/3 + 9/2.

38. f'(x) = 3x² + 6x - 2; (0, 6)

Integrating f'(x) gives:

f(x) = x³ + 3x² - 2x + C

Using the given point (0, 6), we can substitute x = 0 and y = 6 into the equation:

6 = 0 + 0 - 0 + C

C = 6

Therefore, f(x) = x³ + 3x² - 2x + 6.

39. f'(x) = x³ - 2/x² + 2; (1, 3)

Integrating f'(x) gives:

f(x) = (1/4)x⁴ + 2/x + 2x + C

Using the given point (1, 3), we can substitute x = 1 and y = 3 into the equation:

3 = (1/4)(1)⁴ + 2/1 + 2(1) + C

3 = 1/4 + 2 + 2 + C

C = -19/4

Therefore, f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.

40. f'(x) = x⁽⁻¹/²⁾ + x; (1, 2)

Integrating f'(x) gives:

f(x) = 2x⁽¹/²⁾ + (1/2)x² + C

Using the given point (1, 2), we can substitute x = 1 and

y = 2 into the equation:

2 = 2(1)⁽¹/²⁾ + (1/2)(1)² + C

2 = 2 + 1/2 + C

C = 1/2

Therefore, f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.

41. f'(x) = e⁽⁻ˣ⁾ + x; (0, 4)

Integrating f'(x) gives:

f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + C

Using the given point (0, 4), we can substitute x = 0 and y = 4 into the equation:

4 = -e⁽⁻⁰⁾+ (1/2)(0)² + C

4 = -1 + 0 + C

C = 5

Therefore, f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.

42. f'(x) = 3/x - 4; (1, 0)

Integrating f'(x) gives:

f(x) = 3ln|x| - 4x + C

Using the given point (1, 0), we can substitute x = 1 and y = 0 into the equation:

0 = 3ln|1| - 4(1) + C

0 = 0 - 4 + C

C = 4

Therefore, f(x) = 3ln|x| - 4x + 4.

These are the respective functions f(x) obtained from the given derivatives and points.

Learn more about Derivatives here

https://brainly.com/question/29020856

#SPJ4

Answer: 88%

Step-by-step explanation: So, to convert the decimal into a percentage, multiply .88 by 100. And BOOM! you have 88% as your answer.

We spent 88% of your allowance this week.

Since  we know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

To find out what percentage of your allowance you spent,

Divide the amount you spent by your total allowance,

then multiply by 100 to get the percentage.

Here are the steps:

1.  Identify the amount you spent: 0.88

2. Identify your total allowance: 1.00 (assuming your allowance is $1.00) 3. Divide the amount spent by the total allowance,

⇒ 0.88 ÷ 1.00 = 0.88 4.

Multiply the result by 100 to get the percentage,

⇒ 0.88 x 100 = 88%

Therefore, we spent 88% of your allowance this week.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ6

Answer:

y=18(1.15)^x

Step-by-step explanation:

The general formula is

y=a(b)^x, where

a is the initial amount and

b is the growth (1+.15 in our case "an increase of 15%) or

            decay rate (1 -.15 would be if the problem have said it decreased ).

x is the amount of time

y is the amount of money

20.70 = 18 (1.15)^1

The equation is:

y= 18(1.15)^x

Answer:

(2×3)¹

(11×1)¹

Step-by-step explanation:

2×3=6 so 2 to the power 1 is 2 and 3 to the power 1 is 3 so 2×3=6

11×1=11 so 11 to the power 1 is 11 and 1 to the power 1 is 1 so 11×1 =11

Answer:

b value is 3

rise = 3 run = -2

another point could be (2,0)

Step-by-step explanation:

You have the following inequality:

x - 19 ≤ 27

To solve the previous inequality, add 19 both sides and simplify:

x ≤ 27 + 19

x ≤ 46

The graph is:

Answer:

x is less than or equal to 8

Step-by-step explanation:

Answer: 1024!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The domain of this relation (not a function) is x = -5.  The relation is not defined for any other x value.

Answer:

B) {-5}

Step-by-step explanation:

The graph of the line is x=-5 where the domain is {-5} and the range is (-∞,+∞) making B the correct choice

Answer:

B and C

Step-by-step explanation:

The really tough one to get rid of is A. She's right in her method and it sounds like A should be a deal breaker. Suppose however, you make y = 1/x. Now the equation is linear.

y + 3 = 3y            Subtract y from both sides

3 = 3y - y

3 = 2y                  Now divide this by by 2

3/2 = y          

But they are not the same answer!! You've gotten rid of one problem only to create another. Well yes. I never said it was easy getting rid of A. But remember y = 1/x, so x will equal 1 / y.

x = 1/y = 1//3/2 = 2/3

Now they agree.

That's kind of sneaky you might say. That's right it is. But its not wrong. A is not part of the answer.

B is certainly right.

C is correct as well, That's the way the equation is ultimately solved.

D is nonsense. You can do all sorts of things with the letters in equations

The total length of the curve is 24.

and, for the sketch of the curve, to see the attachment.

The sketch of the curve is bottom of the answer.

We have the equation is:

\(x^\frac{2}{3}+y^\frac{2}{3}=4\)

We have to use the interval (-8,8) to find the curve length.

Now since the curve is symmetric, so we will find the length of the curve in (0,8) and multiply the result by 2, so to get the total length, as follows:

\(L=\int\limits^b_a \sqrt{1+(f'(x))^2} \, dx\)

=> \(f(x) =(4-x^\frac{2}{3} )^\frac{3}{2}\)

=> a = 0 , b = 8

=> \(f'(x)=((4-x^\frac{2}{3} )^\frac{3}{2} )'=-\frac{\sqrt{4-x^\frac{2}{3} } }{x^\frac{1}{3} }\)

Thus the length is given by:

\(L=\int\limits^8_0 \sqrt{1+(\frac{\sqrt{4-x^\frac{2}{3} } }{x^\frac{1}{3} } )} \, dx\)

=> \(\int\limits^8_0 {\frac{2}{(x^\frac{2}{3} )^\frac{1}{2} } } \, dx =[3x^\frac{2}{3} ]^8_0=12\)

Hence the total length of the curve is 24.

Learn more about Length of the curve at:

https://brainly.com/question/31376454

#SPJ4